I'll third or fourth the check with local businesses part. We've given away computers before ourselves, and we're just a small family business. I'm sure there are businesses in your area with older computers that they haven't bothered unloading yet.

Also, assuming your club members have computers at home, you could always just pass code back and forth via AIM or IRC chat. You don't physically have to be sitting next to one another in school to collaborate, and since all the Perl reference materials are easily accessed online, you don't have the problem of sharing textbooks either. Plus you have us :) Things would be a lot more difficult if you were trying to learn something like C++.

Incidently, what competition? Have you looked at the USA Computing Olympiad? That's probably the most prestigious programming competition for students in the US, though you do have to know C, C++, Pascal, or Java to compete. I didn't know there were competitions that accepted Perl code.